Abstract: An extended precise integration method for computing the non-stationary response of linear MDOF structure subjected to evolutionary random excitation is proposed. Random loads are first transformed into deterministic loads using Pseudo-excitation algorithm before precise and efficient recursive relations with unified form are constructed by using the precise computing method of Duhamel integration. The avoidance of inverse matrix computing makes the presented method independent to the nature of system matrix or its dynamic matrices, enhancing the numerical stability and expanding its applied scopes. The presented method enjoys the same high numerical precision as HPD-M and a higher efficiency than the expanding precise integration method. Examples are given to show advantages of this method.